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ECE2280 Homework #1 Fall 2011 1. Use: ignore ro, |VBE|=0.7, β=100 VI = 20+0.001sin(20t) For DC analysis, assume that the capacitors are open (a) Solve for the DC currents: a. IB b. IE c. IC + 100Ω 100 1m Vx ≠- 0 1mA C3 (b) Solve for the DC voltages: a. VB b. VE c. Vo IC I1 10V 100Ω 2k 4kΩ Vo 16V VB Q1 C4 100m 1k 100m VI 4kΩ IB (c) Prove or disprove the region of operation you assumed to solve for your answers in (a) and (b)? 1 6kΩ 10k 2V 8V Q2N3904 IE 6.7V 900 VE 4kΩ 6V Rout 2. Use: ignore ro, |VBE|=0.7, β=100 VI = 5+0.001sin(500t) rπ1=2, 000 gm2=50mA/V, and IB2=12.5µ µA For the following hybrid-π equivalent circuit below, find the following values: (a) Rin (input resistance –ignore only the input source, Vsig and include all resistors at the base) (b) Rout (output resistance-include all resistors at the collector{no load is connected}) Vo (c) midband gain, Vsig 2k 3kΩ 2kΩ Vo 100Ω Vsig ~ 2kΩ + + Vπ1 - rπ1 gm1Vπ1 Vπ2 rπ2 6kΩ 1kΩ gm2Vπ2 - Rout Rin 4kΩ 2 4kΩ 3kΩ 3. For the circuit shown below, draw the AC small-signal signal equivalent circuit(use hybrid-π hybrid or model T). Make sure that everything is labeled in terms of the transistor number. (e.g. gm1, vπ2, etc.). Include ro for all transistors. vsig=0.001sin(10t) AC. Assume all capacitors are shorted. +15V R4 vsig R6 -15V 3 +9V 4. Use: Vt=2V kn’(W/L)=4mA/V2 λ=0 VI = 10+0.002sin(20t) For DC analysis, assume that the capacitors act as open (d) Solve for the DC currents: a. I1 b. ID c. IS ID 3k 2k Vo C3 VG 1m VI C4 + ~ (e) Solve for the DC voltages: a. VG b. VS c. Vo NMOS 1k I1 VS 4V 2k 500Ω IS + (f) Verify that the transistor is saturated. R in (g) State the DC bias point. 100m 1.7V R out 500Ω (h) Assuming that the transistor amplification Vo/VI = -7V/V. What is the total (AC and DC) instantaneous output for Vo (VI value stated above). 4 5. Use: Vt=2V kn’(W/L)=3mA/V2 Vsig is an AC source Transistor 1 has DC values: VGS=4V, ID=6mA Transistor 2 has DC values: VGS=5.3V, ID=16.7mA λ=0 (for all transistors) For the following hybrid-π equivalent circuit, find the following values: (a) Rin (input resistance –ignore the input source, Vsig) (b) Rout (output resistance-ignore RL{no load is connected}) Vo (c) midband gain, Vsig 3MΩ 2kΩ + v sig ~ 2MΩ vgs1 g m1v gs1 1kΩ + 1kΩ vgs2 g m2 v gs2 Vo R L = 1kΩ 1kΩ R in R out 5 6 6. For the circuit shown below, draw the AC small-signal equivalent circuit(use hybrid-π or model T). Make sure that everything is labeled in terms of the transistor number. (e.g. gm1, vgs2, etc.). λ=0 for all transistors. vsig=0.005sin(20t) AC. Assume all capacitors are closed for the AC circuit. +15V R3 R8 1mA +10V + 1V Vsig M2 NMOS C3 100m NMOS R6 R1 R7 M1 R2 R9 ~ R4 + 5V R 10 R5 -15V 7 C1 10m 7 (a) Design the cascode amplifier with 2 PMOS transistors for the current source(as shown in class or Fig. 7.11) at a current of 0.1mA with all devices operating at |Vov|=0.25V. All devices have |VA|=4V. Find gm1, the output resistance of the amplifier, Ron, the output resistance of the current source, Rop, the overall output resistance, Rout, and the voltage gain, Av. (b) Use the same circuit with the following DC voltages: VIn=0.8V, VG2=1.2V, VG3=1.3V, VG4=1.7V, and VDD=2.5V. If all devices are matched, that is kn1= kn2= kp3= kp4, and have equal |Vt|=0.5V, what is the overdrive voltage at which the four transistors are operating(Note this is different from part (a))? What is the allowable voltage range at the output? (a) (b) 8 8. Design the cascode amplifier that utilizes 2 PMOS transistors for the current source to have the following specifications: gm1=2mA/V, and Av=-200V/V. Assume that the available fabrication process has V’A=5V/µm for both NMOS and PMOS devices and that µnCox= 4µpCox=400µA/V2 . Use the same channel length L for all devices and operate all four devices at |Vov|=0.2V. Determine the required channel length L, the bias current I, and the W/L ratio for each of four transistors. Assume that suitable bias voltages have been chosen, and neglect the Early effect in determining the W/L ratios. 9 9. A cascode current source formed of two pnp transistors for which β=50 and VA=5V supplies a current of 0.5mA. What is the output resistance? 10. The figures below show four possible realizations of the folded cascode amplifier. Assume that the BJTs have β=100 and that both the BJTs and the MOSFETs have |VA|=5V. Let I=100µA, and assume that the MOSFETs are operating at |VOV|=0.2V. Assume the current sources are ideal. For each circuit determine, Rin, Rout, and the gain Vo/VI. Comment on your results. (a) 10 (b) (c) (d) 11